Let f R2 R2 be given by f(x, y) = (x + xy + y, x...

 

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Let f R2 R2 be given by f(x, y) = (x + xy + y, x y). Note that f(1, 1) = (3,0). = a. Show that f has an inverse in a neighborhood of (3,0). b. Using the first order Taylor polynomial of f-1, approximate the value of f-1 (3.1, -0.2). 5. PROBLEM 5 Consider the surface described by the equation x + y + z xyz = 1. a. Check that this surface can be represented as the graph of some function g= g(x, y) in a neighborhood of the point (0, 0, 1). b. Compute Vg(0,0). Let f R2 R2 be given by f(x, y) = (x + xy + y, x y). Note that f(1, 1) = (3,0). = a. Show that f has an inverse in a neighborhood of (3,0). b. Using the first order Taylor polynomial of f-1, approximate the value of f-1 (3.1, -0.2). 5. PROBLEM 5 Consider the surface described by the equation x + y + z xyz = 1. a. Check that this surface can be represented as the graph of some function g= g(x, y) in a neighborhood of the point (0, 0, 1). b. Compute Vg(0,0).